In article <[EMAIL PROTECTED]>, Stan Brown <[EMAIL PROTECTED]> wrote:
>Here's the part I don't understand: if we agree (as I think we do) >that 95% of all possible random samples lead to a 95% CI that >contains the true value of mu, how can it possibly be incorrect (as >you and others seem to say) to state that the probability of getting >mu in the 95% CI from any _one_ CI is 95%? Perhaps I'm very stupid, >but I just don't see how the statements are not equivalent. Here's one way to see the problem. There are generally MANY procedures for producing intervals that have the property that 95% of the intervals produced contain the true value of mu. Suppose that for your data set, procedure A produces the 95% C.I. (2.2,3.4), whereas procedure B produces the 95% C.I. (3.5,5.1). Are you now going to claim that there is both a 95% chance that mu is between 2.2 and 3.4 AND that there is a 95% chance that mu is between 3.5 and 5.1? Clearly, the logic you give above can't be correct in general. People can sort of get away with thinking that only because the commonly-used procedures for producing confidence intervals have other characteristics (eg, being approximate Bayesian posterior intervals) beyond the property of containing the true parameter value 95% of the time. Radford Neal ---------------------------------------------------------------------------- Radford M. Neal [EMAIL PROTECTED] Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED] University of Toronto http://www.cs.utoronto.ca/~radford ---------------------------------------------------------------------------- . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
